Newsletters are great--to a developer or not, email marketing has a ton of value. At my last company, email was the #1 driver of actions–that was consistent with web and mobile customers as well. But there are a handful of other mediums you can lean on as well. YouTube, Stack Overflow, Twitch, Reddit, Twitter, and LinkedIn all have done pretty well. Also at my last company, someone on my team had the idea to run Google Display ads, and they performed really well. Depending on the size of your organization you may also have a Developer Relations team. Hosting events or webinars/livestreams also tend to perform well. And don't forget your website and your blog, because your developer content is often one of the first places a developer will go to find out information. So think of it like marketing to any customer base: consider where they are in the funnel, think about what actions they need to take to get to the next step, and then leverage the mediums you have at your disposal to push them through the funnel.
I like the spirit of this question, as it's not just relevant to API products but also any product that has a similar onramp due to it being technical. You also touch on something that many inadvertently forget--that it's not enough to launch a product, you also have to think about the "landing" and how to drive continuous engagement.
Here are the few things I've seen teams do: